Bifurcations and chaos of coupled electrical circuits

Zhang-Yao, Chen; Zhang, Xiaofang; Bi, Qinsheng

doi:10.1016/j.nonrwa.2007.02.007

Cited by 12 publications

(5 citation statements)

References 17 publications

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“…In addition to the discovery of a new 4D system, many studies have been carried out to obtain 4D chaotic or hyperchaotic system from 3D chaotic system with various methods (Chen et al, 2006;Jia, 2007). Hence, they have been used for many applications of chaos theory in different fields of engineering and science like ecology (Stone and He, 2007), biology (Itik and Banks, 2010), oscillators (Lu et al, 2020), electrical circuits (Chen et al, 2008;Faradja and Qi, 2020) and so on.…”

Section: Introductionmentioning

confidence: 99%

A new hyperchaotic system from T chaotic system: dynamical analysis, circuit implementation, control and synchronization

Emiroğlu

Akgül

Adıyaman

et al. 2021

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Purpose The purpose of this paper is to develop new four-dimensional (4D) hyperchaotic system by adding another state variable and linear controller to three-dimensional T chaotic dynamical systems. Its dynamical analyses, circuit experiment, control and synchronization applications are presented. Design/methodology/approach A new 4D hyperchaotic attractor is achieved through a simulation, circuit experiment and mathematical analysis by obtaining the Lyapunov exponent spectrum, equilibrium, bifurcation, Poincaré maps and power spectrum. Moreover, hardware experimental measurements are performed and obtained results well validate the numerical simulations. Also, the passive control method is presented to make the new 4D hyperchaotic system stable at the zero equilibrium and synchronize the two identical new 4D hyperchaotic system with different initial conditions. Findings The passive controllers can stabilize the new 4D chaotic system around equilibrium point and provide the synchronization of new 4D chaotic systems with different initial conditions. The findings from Matlab simulations, circuit design simulations in computer and physical circuit experiment are consistent with each other in terms of comparison. Originality/value The 4D hyperchaotic system is presented, and dynamical analysis and numerical simulation of the new hyperchaotic system were firstly carried out. The circuit of new 4D hyperchaotic system is realized, and control and synchronization applications are performed.

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Section: Introductionmentioning

confidence: 99%

A new hyperchaotic system from T chaotic system: dynamical analysis, circuit implementation, control and synchronization

Emiroğlu

Akgül

Adıyaman

et al. 2021

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“…During the past two decades, many chaotic systems have been proposed and their complex behaviors have also been Y. Farid (B) • T. V. Moghaddam Advanced Power and Control Systems Lab., EE Department, Imam Khomeini International University, Qazvin, Iran e-mail: y.farid.e.control@gmail.com T. V. Moghaddam e-mail: tahminevedadi@gmail.com widely studied [1][2][3]. In recent years, many engineering applications of chaotic systems are discussed such as secure communication, digital communication, power electronic devices, power quality, biological systems, chemical reactions analysis and information processing [4][5][6].…”

Section: Introductionmentioning

confidence: 99%

Generalized projective synchronization of chaotic satellites problem using linear matrix inequality

Farid

Moghaddam

2014

Int. J. Dynam. Control

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In this paper, a systematic design procedure for generalized projective synchronization between two identical chaotic satellites systems based on feedback control theory is proposed. This method is developed based on suitable feedback control, combined with the Lyapunov stability theory and linear matrix inequality formulation as a solution of the optimal problem. Two necessary and sufficient conditions for the asymptotic stability of the error dynamic system are obtained. Compared with the predictive-based control method, the proposed method shows comparable and superior performance. The effectiveness of the obtained results is illustrated by numerical simulations.

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“…Since the first chaotic attractor was found by Lorsenz in 1963, the theory of chaos has been developing rapidly. The topics of chaos and chaotic control are growing rapidly in many different fields such as biological systems and ecological and chemical systems [1][2][3][4][5]. The desirability of chaos depends on the particular application.…”

Section: Introductionmentioning

confidence: 99%

Delayed Feedback Control and Bifurcation Analysis of an Autonomy System

Wang

Zhao

Kong

2013

Abstract and Applied Analysis

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An autonomy system with time-delayed feedback is studied by using the theory of functional differential equation and Hassard’s method; the conditions on which zero equilibrium exists and Hopf bifurcation occurs are given, the qualities of the Hopf bifurcation are also studied. Finally, several numerical simulations are given; which indicate that when the delay passes through certain critical values, chaotic oscillation is converted into a stable state or a stable periodic orbit.

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Bifurcations and chaos of coupled electrical circuits

Cited by 12 publications

References 17 publications

A new hyperchaotic system from T chaotic system: dynamical analysis, circuit implementation, control and synchronization

A new hyperchaotic system from T chaotic system: dynamical analysis, circuit implementation, control and synchronization

Generalized projective synchronization of chaotic satellites problem using linear matrix inequality

Delayed Feedback Control and Bifurcation Analysis of an Autonomy System

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